Construction of N-body initial data sets in general relativity

Given a collection of N solutions of the (3+1) vacuum Einstein constraint equations which are asymptotically Euclidean, we show how to construct a new solution of the constraints which is itself asymptotically Euclidean, and which contains specified sub-regions of each of the N given solutions. This generalizes earlier work which handled the time-symmetric case, thus providing a construction of large classes of initial data for the many body problem in general relativity

Deformation of Scalar Curvature and Volume

The stationary points of the total scalar curvature functional on the space of unit volume metrics on a given closed manifold are known to be precisely the Einstein metrics. One may consider the modified problem of finding stationary points for the volume functional on the space of metrics whose scalar curvature is equal to a given constant. In this paper, we localize a condition satisfied by such stationary points to smooth bounded domains. The condition involves a generalization of the static equations, and we interpret solutions (and their boundary values) of this equation variationally. On domains carrying a metric that does not satisfy the condition, we establish a local deformation theorem that allows one to achieve simultaneously small prescribed changes of the scalar curvature and of the volume by a compactly supported variation of the metric. We apply this result to obtain a localized gluing theorem for constant scalar curvature metrics in which the total volume is preserved. Finally, we note that starting from a counterexample of Min-Oo's conjecture such as that of Brendle-Marques-Neves, counterexamples of arbitrarily large volume and different topological types can be constructed.Comment: All comments welcome! Published version: Math. Ann. (to appear

Construction of N-body time-symmetric initial data sets in general relativity

Given a collection of N asymptotically Euclidean ends with zero scalar curvature, we construct a Riemannian manifold with zero scalar curvature and one asymptotically Euclidean end, whose boundary has a neighborhood isometric to the disjoint union of a specified collection of sub-regions of the given ends. An application is the construction of time-symmetric solutions of the constraint equations which model N-body initial data

On Existence of Static Metric Extensions in General Relativity

Motivated by problems related to quasi-local mass in general relativity, we study the static metric extension conjecture proposed by R. Bartnik \cite{Bartnik_energy}. We show that, for any metric on $\bar{B}_1$ that is close enough to the Euclidean metric and has reflection invariant boundary data, there always exists an asymptotically flat and scalar flat {\em static} metric extension in $M = \R^3 \setminus B_1$ such that it satisfies Bartnik's geometric boundary condition \cite{Bartnik_energy} on $\partial B_1$.Comment: 20 page

Immigration policies in times of crisis a comparative study of the united states and australia

Although they are two very similar net immigration countries, Australia and the US took very different approaches to immigration policy adoption and implementation and to immigration control, in the last two decades of the 20th century. The literature explains these different approaches by invoking the influence of interest groups, human rights initiatives and the reaction of state institutions to public pressure. This paper proposes an alternative explanation for the difference in immigration policy and control: crisis. Crisis, or a sense thereof, is what leads the population to mobilize and to put pressure on the government for more efficient policies and stricter immigration controls. The historical analysis of major immigration policies passed in Australia and the United States in the 1800s and 1990s, reveals that, indeed, wars, social pressures, internal conflicts, and, indeed, a generalized sense of crisis was key to major changes in immigration policy in both countries

Sweatshops, Harm and Exploitation: A Proposal to Operationalise the Model of Structural Injustice

In this article, I firstly discuss the person-affecting view of harm, distinguishing between the liability and the structural models of responsibility, and also explaining why it is unsatisfactory, from a moral point of view, to interpret a given harm as a loss with respect to a diachronic baseline. Then, I take sweatshops as an example and I entertain two further issues that are related to the assessment of harm and that are necessary for operationalising a comprehensive model of responsibility, that takes into account both liability and structural injustice. The first one is how to interpret harm when it is coexistent with a diachronic benefit and/or the parties involved in the social structures leading to harm seek to unload their responsibility by hiding behind a cooperative deadlock. The second one is how far along the chain of actions leading to harm can structural responsibility be extended